STD 11 - 10.1 circle and system of circle — JEE STD 11 Science — Question

$\therefore $ Let ‘$r$’ be the radius of circle and ‘$a$’ be the side of square

$\therefore $ $2\pi \,r = 4a \Rightarrow a = \frac{{\pi \,r}}{2}$

$\therefore $ Area of square ${C_1}(3,\; - 3)$ ${a^2} = \frac{{{\pi ^2}{r^2}}}{4}$
and area of circle = $\pi \,{r^2}$

$\therefore $ $\frac{{{\rm{Area\ of\ circle}}}}{{{\rm{Area\ of\ square}}}} = \frac{{\pi \,{r^2}}}{{{\pi ^2}{r^2}/4}} = \frac{4}{\pi } > 1$.

Thus, area of circle is larger than area of square.